The class \(\mathcal {P}\)  of planar graphs is minor-closed, with excluded minors the complete graphs \(K_5\)  and \(K_{3,3}\)  which are both 2-connected. Other minor-closed graph classes with 2-connected excluded minors include for example series-parallel graphs and outerplanar graphs. Every proper minor-closed class \(\mathcal {A}\)  of graphs with 2-connected excluded minors has a growth constant [1]}, [2]}, and it is easy to see that all connected graphs in \(\mathcal {A}\)  are free for \(\mathcal {A}\) . Thus from Theorem REF  we obtain the following result.
